Partial Fractions | Mathematico

The method of partial fractions allows us to separate a fraction into two, simpler fractions like this:

\frac{3 x + 1}{x^{2} + 2 x - 3} = \frac{2}{x + 3} + \frac{1}{x - 1}

Going from right-to-left is just adding together two fractions and is easier; going from left-to-right is trickier, and that's what partial fractions is all about.

Use the method of partial fractions to decompose the following fractions:

$\frac{17}{3 x^{2} + 13 x - 10}$
$\frac{4 x^{2} + 5 x - 21}{(x + 2) (x - 3) (x - 1)}$
$\frac{2 x^{2} + 8 x + 10}{(x + 1) (x + 2)^{2}}$